The chromatic number of the $n$-dimensional Euclidean space, denoted $\chi(\mathbb{R}^n)$, is the minimum number of colors that can be assigned to the points of $\mathbb{R}^n$ so that no two points at distance one receive the same color. In this talk we present better lower bounds for $\chi(\mathbb{R}^n)$ for several small values of $n$.
Joint work with Geoffrey Exoo, Indiana State University.